The Andorians have been tight-lipped about the reproductive crisis for decades. Wasn't it only in Andor: Paradigm that it really emerged to the Federation at large as a massive problem?
The precise details, maybe, but the fact that something was up would be evident to non-Andorians even without pirivleged information.
Population issues are a hobby of mine; I
post about population-related issues extensively on a group blog, even. You can deduce quite a few things from basic information.
The former West Germany and France have roughly similar levels of fertility within marriage. Why is fertility so much higher in France than in West Germany? Non-marital fertility is much higher in France than in the former West Germany, where women in their reproductive ages almost have to make a choice between having children within marriage in a fairly conservative milieu (more conservative than France) and opting to have careers but to forego parenthood.
The above analysis took some number-crunching, but the raw numbers and interpretations are available. National statistical institutes in 21st century Earth regularly produce updates containing detailed information on demographic issues of all kinds, including data on specific patterns of family formation: the age of first childbirth, the sorts of relationships that are common, the number of children born into different types of relationships, and so on. This is all public domain information here on Earth, not too difficult to find if you're interested in finding it.
Andorians seem to have been suffering negative population growth for some time before Andor's secession, at least a couple of generations (though apparently not during the 22nd century). The Andorians reorganized their civilization to encourage the remaining cohorts of Andorian young are placed into arranged marriages at very early ages and to have as many children in the brief window of fertility as possible. Even if no one in Andorian civilization talked about their species' issues at all--unlikely, given how frequently demographic issues are raised in public discourse here on Earth, in connection with issues as various as pension plan funding to ethnic identity--non-Andorian observers would pick up on the shifts in Andorian family formation patterns and make informed speculation about what these shifts were supposed to do. That these radical fertility-maximizing shifts didn't stop negative population growth would also have been noticed. Basic tables would have shown that a rapid spike in the death rate wasn't responsible.
The Andorians may not have talked to non-Andorians about the true extent of their species' problems. Probably they didn't. (This implies, BTW, that the Andorians have been very isolated within the Federation for quite some time.) Even before the Andorians made their formal request for help, it would have been evident to anyone interested in the subject of the demographcis of one of the Federation's founding species that something was off.
Had they trusted their own allies instead of being scared about how they would be treated or whatever, Federation scientists might have been able to assist earlier, perhaps even during the Taurus Metagenome research.
Especially if the Taurus Metagenome had obviously and immediately relevant applications to the fertility crisis.
All I can suggest, by way of an explanation considering that Andorians were involved in the research, is two things.
1. The applications of the Taurus Metagenome to the Andorian fertility crisis are not obvious, or were not obvious in the mid- to late-23rd century.
2. Things suddenly became much worse for the Andorians after the Metagenome was classified.
There's evidence for both arguments. Cracking the Shedai genetic code was problematic, and not only for political reasons. At the same time, in the 22nd century Shran is shown in the nvoels as having been excluded from quad formation and opting for a relationship with another Andorian similarly excluded from quad formation.